Cayley-Hamilton theorem
CayleyHamiltonTheorem
2002-02-05 20:18:09
2002-02-05 20:39:42
Theorem
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
%\usepackage{psfrag}
%\usepackage{graphicx}
%\usepackage{xypic}
Let $T$ be a linear operator on a finite-dimensional vector space $V$, and let $c(t)$ be the characteristic polynomial of $T$. Then $c(T)=T_0$, where $T_0$ is the zero transformation. In other words, $T$ satisfies its own characteristic equation.